Cv Liquid Flow Calculator

Background.

Every control valve, ball valve and solenoid valve sold for liquid service has a flow coefficient, Cv, on its data sheet. It is the valve's capacity reduced to one number: the US gallons per minute of 60 °F water that pass through it with a pressure drop of 1 psi across it. A valve with a Cv of 10 passes 10 gpm of water at a 1 psi drop; one with a Cv of 100 passes ten times as much under the same conditions.

Real systems rarely run at exactly 1 psi, and they seldom carry plain water, so the coefficient has to be scaled. Flow through a restriction rises with the square root of the pressure drop and falls with the square root of the liquid's specific gravity: Q = Cv × √(ΔP ÷ SG). The square root is what catches people out. Quadrupling the pressure drop only doubles the flow, so a valve that is a little too small cannot be rescued by pushing much more pressure through it.

This is the basic US-unit liquid sizing relation found in control-valve handbooks and the ISA-75.01.01 standard, and it holds while flow through the valve is fully turbulent and stays liquid. It breaks down when the pressure inside the valve falls low enough for the liquid to start boiling: the flow cavitates or flashes and eventually chokes, and raising the pressure drop further adds noise and damage but no more flow. Viscous liquids, reducers fitted directly to the valve body, and gases or steam all need corrections or different equations that are not applied here.

Within those limits it is the quickest way to check whether an installed valve can pass the flow you need, or how much flow you lose when the supply pressure drops.

What is cv liquid flow calculator?

The result is the volumetric flow rate of a liquid through a valve, in US gallons per minute, predicted from the valve's flow coefficient Cv, the pressure difference between its inlet and outlet in psi, and the liquid's specific gravity — its density relative to water, so water is 1. Because Cv is defined with water at 60 °F and a 1 psi drop, water at a 1 psi drop returns exactly the Cv value.

Specific gravity belongs at the flowing temperature. Water at 80 °C has a specific gravity of about 0.97, which raises the predicted flow by only about 1.4%, so temperature seldom matters for water; it matters more for light hydrocarbons, whose density shifts faster as they warm. Rough values are 0.84 for diesel, 1.025 for seawater and above 1 for brines and glycol mixtures. Pipe size, by contrast, says little about capacity: a needle valve and a full-port ball valve with the same 1-inch connections can differ in Cv many times over, so it is the coefficient, not the connection size, that should be compared when choosing between valves.

How to use this calculator.

1. 01Enter the Valve flow coefficient Cv from the manufacturer's data sheet, for the opening you care about. The rated figure usually describes a fully open valve; a throttled control valve has a smaller effective Cv.
2. 02Enter the Pressure drop in psi across the valve itself — inlet pressure minus outlet pressure at the valve — not across the whole pipe run. To convert from bar, multiply by 14.504.
3. 03Enter the Liquid specific gravity at the flowing temperature: 1 for water, below 1 for lighter liquids such as most oils and fuels, above 1 for brines and other dense fluids.
4. 04Read the flow in US gallons per minute (multiply by 3.785 for litres per minute) and check the model-scope note: if the valve may be cavitating or the liquid is thick, real flow will be lower than shown.

The formula.

Q = Cv × √(ΔP ÷ SG), with Q in US gallons per minute, ΔP in pounds per square inch and SG dimensionless. There is no hidden constant because Cv is defined in exactly those units: at ΔP = 1 psi and SG = 1 the square root is 1 and Q equals Cv. Flow is directly proportional to Cv but depends on the square root of the other two terms, so doubling the pressure drop raises flow by only √2, about 41%, and a liquid 20% denser than water flows about 8.7% more slowly. Rearranged, the same relation sizes a valve: Cv = Q × √(SG ÷ ΔP). The metric counterpart, Kv, is defined in cubic metres per hour of water at a 1 bar drop, and Cv ≈ 1.156 × Kv.

The square root comes from an energy balance across the valve's narrowest passage. The pressure difference accelerates the liquid and most of it is lost to turbulence downstream, so ΔP = K × ρv² ÷ 2 for a loss coefficient K; solving for velocity and multiplying by the flow area gives Q proportional to A × √(ΔP ÷ (K × ρ)). Cv bundles the area, the loss coefficient and the unit conversions into one measured number, which is why it converts to a resistance coefficient for pipe-network work: for a valve of inside diameter d in inches, Cv = 29.9 × d² ÷ √K.

The same derivation marks the limits. It assumes fully turbulent flow, so that K, and therefore Cv, does not change with flow rate. It also assumes the liquid stays liquid. The ISA sizing standard caps the useful drop at FL² × (P1 − FF × Pv), where FL is the valve's liquid pressure-recovery factor from the manufacturer, P1 the absolute inlet pressure, Pv the vapour pressure of the liquid and FF a factor close to 0.96 for water at ordinary temperatures. For room-temperature water at 100 psia and a valve with FL = 0.9, the cap is about 80.72 psi; beyond it flow is choked. High-recovery designs such as ball and butterfly valves have lower FL values than globe valves and reach the cap at smaller drops.

A worked example.

Frequently asked questions.

References& sources.

1. [1]Emerson, Control Valve Handbook, 6th ed.
2. [2]Swagelok, Valve Sizing Technical Bulletin.
3. [3]BIPM, The International System of Units (SI Brochure), 9th ed., version 3.01, coherent derived units and quantity equations.
4. [4]NIST Special Publication 811, Guide for the Use of the International System of Units, 2008 edition.
5. [5]ISA, Control Valve Sizing Equations, ANSI/ISA-75.01.01 (bibliographic standard).